Triple
T11412034
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Methods of Representation Theory |
E270393
|
entity |
| Predicate | covers |
P1393
|
FINISHED |
| Object |
Maschke’s theorem
Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
|
E924213
|
NE FINISHED |
How this triple was built (4 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Maschke’s theorem | Statement: [Methods of Representation Theory, covers, Maschke’s theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Maschke’s theorem Context triple: [Methods of Representation Theory, covers, Maschke’s theorem]
-
A.
Peter–Weyl theorem
The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
-
B.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
C.
Jordan–Hölder theorem
The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
-
D.
Cayley–Hamilton theorem
The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
-
E.
Artin–Wedderburn theorem
The Artin–Wedderburn theorem is a fundamental result in ring theory that classifies all semisimple rings as finite direct products of matrix rings over division rings.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Maschke’s theorem Triple: [Methods of Representation Theory, covers, Maschke’s theorem]
Generated description
Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Maschke’s theorem Target entity description: Maschke’s theorem is a fundamental result in representation theory stating that every finite group representation over a field of characteristic not dividing the group order is completely reducible into a direct sum of irreducible representations.
-
A.
Peter–Weyl theorem
The Peter–Weyl theorem is a fundamental result in representation theory and harmonic analysis that decomposes square-integrable functions on a compact topological group into a direct sum of finite-dimensional irreducible unitary representations.
-
B.
Schur–Weyl duality
Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
-
C.
Jordan–Hölder theorem
The Jordan–Hölder theorem is a fundamental result in group theory stating that any two composition series of a finite group have the same length and the same (up to order and isomorphism) simple factor groups.
-
D.
Cayley–Hamilton theorem
The Cayley–Hamilton theorem is a fundamental result in linear algebra stating that every square matrix satisfies its own characteristic polynomial.
-
E.
Artin–Wedderburn theorem
The Artin–Wedderburn theorem is a fundamental result in ring theory that classifies all semisimple rings as finite direct products of matrix rings over division rings.
- F. None of above. chosen
Provenance (5 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69d6aaddeaa8819088b30ef7b50598c9 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d8015017d08190b4020c76545556d6 |
completed | April 9, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e5b855f0508190a2e57ef9407ddb1a |
completed | April 20, 2026, 5:23 a.m. |
| NEDg | Description generation | batch_69e5c28d3824819097ff84cb4e13c923 |
completed | April 20, 2026, 6:07 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e5c451c6c88190bcbb1f54ede35d29 |
completed | April 20, 2026, 6:14 a.m. |
Created at: April 8, 2026, 9:34 p.m.